Question: Find
\[\binom{100}{0} - \binom{100}{1} + \binom{100}{2} - \dots + \binom{100}{100}.\]
Answer: By the Binomial Theorem,
\[(x + y)^{100} = \binom{100}{0} x^{100} + \binom{100}{1} x^{99} y + \binom{100}{2} x^{98} y^2 + \dots + \binom{100}{100} y^{100}.\]Setting $x = 1$ and $y = -1,$ we get
\[\binom{100}{0} - \binom{100}{1} + \binom{100}{2} - \dots + \binom{100}{100} = \boxed{0}.\]